• After solving a system of linear equations, how can you check your answer to determine whether it is correct? Demonstrate the process of checking an answer with an example
Merely insert the values to see if they work.
To check if your solution to a system of linear equations is correct, you need to substitute the values you found back into the original equations and see if both sides are equal. Here's a step-by-step process to demonstrate how to check an answer using an example:
Example:
Let's say we have the following system of linear equations:
Equation 1: 2x + 3y = 7
Equation 2: 5x - 2y = 8
Step 1: Solve the system of linear equations to find the values for x and y. Let's assume the solution is x = 2 and y = 1.
Step 2: Substitute the values of x and y back into the original equations.
For Equation 1:
2(2) + 3(1) = 7
4 + 3 = 7
7 = 7
For Equation 2:
5(2) - 2(1) = 8
10 - 2 = 8
8 = 8
Step 3: Compare the left side of each equation with the right side. If both sides are equal, then your solution is correct.
In this case, both sides of Equation 1 and Equation 2 are equal. Hence, the solution (x = 2, y = 1) is correct.
By following this process, you can check whether your solution to a system of linear equations is accurate or not. If the values satisfy all the original equations, then you have found the correct solution. If not, you may need to recheck your work or consider alternative methods to find the solution.